let t = the number of students who live in town.
let f = the number of students who live on a farm.
the total number of students in the school = 200.
b = number of boys.
g = number of girls.
3/5 of the students are boys, therefore 3/5 * 200 = 120 boys in the school.
that means that 2/5 of the students are girls, therefore 2/5 * 200 = 80
girls.
you are given that all of the students live either in town or on a farm.
that means that t + f = 200.
one third of the students who live on a farm are girls.
that means that 1/3 * f = g.
you are also given that 3/4 of the girls live in town.
that means that 3/4 * g = t.
you have determined that 120 of the students are boys and 80 of the students are girls.
since 3/4 of the girls live in town, then 3/4 * 80 = 60 girls live in town.
that means that 20 girls live on a farm.
since 1/3 of the students who live on a farm are girls, that means that:
1/3 * f = 20
solve for f to get f = 60 students who life on a farm.
since 20 of them are girls, the rest have to be boys.
that means that 40 boys live on a farm.
since 40 boys live on a farm, that means that 80 boys must live in town.
the total number of students who live on a farm is 60.
the total number student who live in town = 200 - 60 = 140.
the final figures are:
120 boys and 80 girls for a total of 200 students
40 boys and 20 girls on the farm for a total of 60 students on the farm.
80 boys and 60 girls in town for a total of 140 students in town.
that should be your solution.
to confirm, go through the problem again with these numbers to see if they confirm that the solution is correct.
the numbers in tabular form are:
town farm total
boys 80 40 120
girls 60 20 80
total 140 60 200
ratio of girls to students on farm = 20/60 = 1/3.
ratio of girls in town to total girls = 60/80 = 3/4.
20 girls live on farm.
80 boys live in town.
fraction of all students who live in town is 140 / 200 = 7/10.